# Homework Help: Projectile Motion- magnitude of final velocity

1. Apr 3, 2015

### Nelson2436

1. The problem statement, all variables and given/known data
Consider a cannon on a 50m high cliff. The cannon shoots a cannonball with an initial speed of 200m/s at an angle of 30°, causing the cannonball to land 41m away from the cannon. What is the magnitude of the velocity of the cannonball the instance just before it hits the ground?
a) -205m/s
b) 205m/s
c) 173m/s
d) 267m/s

2. Relevant equations
ax=0 ay=-g
1) Xf=Xi+Vixt
2) Yf=Yi+Viyt-½gt2
3) Vfy=Viy-gt
4) Vfy2=Viy2-2g(Yf-Yi)

3. The attempt at a solution
Vi=200m/s
Vix=200cos30 Viy=200sin30
Xi=0m Yi= 50m
Xf=41m Yf= 0m

In order to find the magnitude of Vf, I need to find its components, Vfx and Vfy. In projectile motion, Vfx=Vix=200cos30, so I just need to find Vfy.

Using equation 1 to find time: t=41/(200cos30)= 0.2367s
I then plugged time into equation 3 to find Vfy=200sin30-(9.8)(0.2367)= 97.68m/s

So Vfx=200cos30= 173.2m/s and Vfy= 97.68m/s so
Vf= √(Vfx2+Vfy2)= √(173.22+97.682)= 199 m/s

I don't see where I'm going wrong, but 199m/s is not one of the 4 multiple choice answers. I would greatly appreciate any help.

2. Apr 3, 2015

### TSny

Hi, Nelson2436. Welcome to PF!

The 41 m given in the problem just doesn't seem right. You should actually be able to find where the cannon ball lands from the other information given in the problem. Did you state the problem exactly as given?

3. Apr 3, 2015

### Nelson2436

Yes, I stated the problem exactly as given. This problem is driving me crazy.